*> \brief \b DLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLA_GBRPVGRW + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * DOUBLE PRECISION FUNCTION DLA_GBRPVGRW( N, KL, KU, NCOLS, AB, * LDAB, AFB, LDAFB ) * * .. Scalar Arguments .. * INTEGER N, KL, KU, NCOLS, LDAB, LDAFB * .. * .. Array Arguments .. * DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLA_GBRPVGRW computes the reciprocal pivot growth factor *> norm(A)/norm(U). The "max absolute element" norm is used. If this is *> much less than 1, the stability of the LU factorization of the *> (equilibrated) matrix A could be poor. This also means that the *> solution X, estimated condition numbers, and error bounds could be *> unreliable. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The number of linear equations, i.e., the order of the *> matrix A. N >= 0. *> \endverbatim *> *> \param[in] KL *> \verbatim *> KL is INTEGER *> The number of subdiagonals within the band of A. KL >= 0. *> \endverbatim *> *> \param[in] KU *> \verbatim *> KU is INTEGER *> The number of superdiagonals within the band of A. KU >= 0. *> \endverbatim *> *> \param[in] NCOLS *> \verbatim *> NCOLS is INTEGER *> The number of columns of the matrix A. NCOLS >= 0. *> \endverbatim *> *> \param[in] AB *> \verbatim *> AB is DOUBLE PRECISION array, dimension (LDAB,N) *> On entry, the matrix A in band storage, in rows 1 to KL+KU+1. *> The j-th column of A is stored in the j-th column of the *> array AB as follows: *> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) *> \endverbatim *> *> \param[in] LDAB *> \verbatim *> LDAB is INTEGER *> The leading dimension of the array AB. LDAB >= KL+KU+1. *> \endverbatim *> *> \param[in] AFB *> \verbatim *> AFB is DOUBLE PRECISION array, dimension (LDAFB,N) *> Details of the LU factorization of the band matrix A, as *> computed by DGBTRF. U is stored as an upper triangular *> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, *> and the multipliers used during the factorization are stored *> in rows KL+KU+2 to 2*KL+KU+1. *> \endverbatim *> *> \param[in] LDAFB *> \verbatim *> LDAFB is INTEGER *> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleGBcomputational * * ===================================================================== DOUBLE PRECISION FUNCTION DLA_GBRPVGRW( N, KL, KU, NCOLS, AB, \$ LDAB, AFB, LDAFB ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER N, KL, KU, NCOLS, LDAB, LDAFB * .. * .. Array Arguments .. DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I, J, KD DOUBLE PRECISION AMAX, UMAX, RPVGRW * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN * .. * .. Executable Statements .. * RPVGRW = 1.0D+0 KD = KU + 1 DO J = 1, NCOLS AMAX = 0.0D+0 UMAX = 0.0D+0 DO I = MAX( J-KU, 1 ), MIN( J+KL, N ) AMAX = MAX( ABS( AB( KD+I-J, J)), AMAX ) END DO DO I = MAX( J-KU, 1 ), J UMAX = MAX( ABS( AFB( KD+I-J, J ) ), UMAX ) END DO IF ( UMAX /= 0.0D+0 ) THEN RPVGRW = MIN( AMAX / UMAX, RPVGRW ) END IF END DO DLA_GBRPVGRW = RPVGRW END